Four methods are presented for optimizing filters in the normalized peak ripple magnitude (NPRM) sense. Two of the methods belong to the passband gain sectioning technique. The other two methods make use of the objective function f = δ - αb. Several heuristic methods for determining α are also presented. The NPRM is an important performance measure; the absolute peak ripple magnitude and passband gain are less important. In these applications, the passband gain need not be fixed at unity but should be a continuous variable to be optimized. Nevertheless, an upper and a lower bound on the passband gain should be imposed to satisfy overflow and roundoff noise performance requirements.